Stationary points of plane forms

Stationary Points and Equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path ...

Stationary Points of Transformation Groups.

Singular Points of Plane Curves

ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...

Poincar E Renormalized Forms and Regular Singular Points of Vector Elds in the Plane

We discuss the local behaviour of vector elds in the plane R 2 around a singular point (i.e. a zero), on the basis of standard (Poincar e-Dulac) normal forms theory, and from the point of view of Poincar e renormalized forms 28]. We give a complete classiication for regular singular points and provide explicit formulas for non-degenerate cases. A computational error for a degenerate case of cod...

Poincaré and Lie renormalized forms for regular singular points of vector fields in the plane

We discuss the local behaviour of vector fields in the plane R around a regular singular point, using recently introduced reduced normal forms, i.e. Poincaré and Lie renormalized forms [30, 31, 32]. We give a complete classification, and provide explicit formulas, using Poincaré renormalized forms for non-degenerate cases, and Lie ones for certain degenerate cases. Both schemes are completely a...